• SJSU Singular Matrix Database
  • Matrix group: Pothen
  • Click here for a description of the Pothen group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups

  • Matrix: Pothen/sphere2
  • Description: sphere2, with coordinates. From NASA, collected by Alex Pothen
  • download as a MATLAB mat-file, file size: 2 KB. Use SJget(218) or SJget('Pothen/sphere2') in MATLAB.
  • download in Matrix Market format, file size: 1 KB.
  • download in Rutherford/Boeing format, file size: 1 KB.


    Routine svd from Matlab (R2008a) used to calculate the singular values.


    Pothen/sphere2 graph

    Matrix properties (click for a legend)  
    number of rows66
    number of columns66
    structural full rank?yes
    structural rank66
    numerical rank 64
    dimension of the numerical null space2
    numerical rank / min(size(A))0.9697
    Euclidean norm of A 6.8771
    calculated singular value # 640.074631
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 653.758e-016
    gap in the singular values at the numerical rank:
    singular value # 64 / singular value # 65
    calculated condition number4.004e+017
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    editorG. Kumfert, A. Pothen
    kindstructural problem
    2D/3D problem?yes

    Additional fieldssize and type
    coordfull 66-by-3

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))682 650
    Cholesky flop count8.6e+003 7.5e+003
    nnz(L+U), no partial pivoting1,298 1,234
    nnz(V) for QR, upper bound nnz(L) for LU807 820
    nnz(R) for QR, upper bound nnz(U) for LU1,368 1,305

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.